Since AnsPress 4.1.0, you can easily add new fields to existing form. For more detail about Form and field, check New form and validation classes introduced in AnsPress 4.1.0.
Below snippet shows how to add a new field in question form for allowing users to upload a PDF file. Notice
allowed_mimes in field, you can change it to any mimes type as per your requirement.
AnsPress does not save field or upload files by itself but it provide helper functions to make it easier. we just need to hook after a question is processed and add a post meta for later use:
Now, pdf url can be fetched anywhere using
wp_get_attachment_url( get_post_meta( $post_id, 'my_custom_pdf', true ) ).